Question

A pendulum swings through an angle of ${60}^\circ$ and describes an arc $8.8$ cm in length. Find the length of the pendulum.

Answer 1

Let angle of pendulum = ß = 60°
We know that,


$\frac{ \beta }{360} \pi {r}^{2} = \frac{1}{2} lr$

Where, r is the length of pendulum, and l is the length of arc.
So, substituting values, we get,

$\frac{1}{6} \times \frac{22}{7} \times {r}^{2} \: = \frac{1}{2} (8.8)(r) \\ r = (4.4) \times 6 \: \times \frac{7}{22} \\ r \: = 8.4$
Therefore, length of pendulum = 8.4 cm

Answer 2

☯ Dear User ☯

▶ Question: A pendulum swings through an angle of 60° and describes an arc 8.8 cm in length. Find the length of the pendulum.

▶Method of Solution:

In this Question, It is given that A pendulum swings through an angle of 60° and describes an arc 8.8 cm in length. ↩

Now, From Statement We have obtained!

Length of arc = 8.8 cm

Value of ∅ = 60°

Changing ∅ into Radian measure!

Radian = π/180° × Degree

Radian = 60°π/180

•°• Radian = π/3 Radian

----------------------------------------------------------

↪ We know that : [ l = ∅r ]

Substitute the obtained value in Formula!

↪l = ∅r

↪l = π/3 ÷ 8.8

=> Length = 8.8×3 ÷ (π)

=> Length = 26.4 ÷π

=> Length of Pendulum = 8.4 cm

↪↪Hence, Required Length of Pendulum is (8.4 cm)↩↩

↪↪↪↪↪↪↪↪↪↪↪↪↪↪↪↪↪↪↪↪

Method : (ii)

↪↪We know that Formula of Area of arc length is 2πr∅/360°↪↪

↪Substitute the obtained value in Equation!↩

↪2πr∅/360° = 8.8

↪2×22/7× 60°/360° = 8.8

↪44/7×1/6 = 8.8

↪8.4 Centimeters

Hence, Required Value of Length of Pendulum is 8.4 centimeters